We further develop the theory of Urbach tails (Urbach rule). The presented theory of the light absorption below the band edge is based on the assumption that the light absorption below the band edge is due to the tunnel-activated transitions of the lattice. Each type of tunnel-activational transitions corresponds to a class of multiphonon instantons, which is associated with the regime of light absorption. The theory presented predicts the existence of certain singularities in the Urbach tail. We propose an experiment to detect these kinds of singularities. We have made calculations on the model of Frenkel excitons interacting with nonpolar deformational optical phonons in three-dimensional crystals and determined the ‘‘phase diagram’’ of different regimes of light absorption. The possibility of experimental studies of these diagrams in the Urbach tail is discussed.